Ariel Almendral Vazquez

This user manual describes the COHIBA surface modeling software. It consists of: Part I Introduction: Basic ideas and terminology Part II User manual: Usage, input data, and results Part III Tutorials: Special topics such as volumes, simulation, and faults Part IV Reference manual: Descriptions of all COHIBA model file elements Part V Theory: Methods used by COHIBA Part VI Appendix: Release notes, known issues, references, list of acronyms, tables and figures, and an index

This user manual describes the COHIBA surface modeling software. It consists of: Part I Introduction: Basic ideas and terminology Part II User manual: Usage, input data, and results Part III Tutorials: Special topics such as volumes, simulation, and faults Part IV Reference manual: Descriptions of all COHIBA model file elements Part V Theory: Methods used by COHIBA Part VI Appendix: Release notes, known issues, references, list of acronyms, tables and figures, and an inde

Abstract Logging-while-drilling (LWD) tools transmit formation data in real-time to the surface as the drill bit moves through the subsurface. LWD is particularly valuable in horizontal wells where it minimizes the risk of getting off course and drilling into undesired formations. The introduction of ultra-deep azimuthal resistivity (UDAR) technology has improved the process of drilling horizontal wells (Antonsen et al. 2022), but its value is limited to reservoirs where important resistivity contrasts are observed. When this is not the case, a classical LWD measure like gamma ray, becomes crucial for well placement. The interpretation of well logs is difficult, however, and error prone whenever manual work is involved. In this paper, we present a method for consistently integrating the structural model with LWD measurements while drilling. This approach enables estimation of the distance between the drill bit and nearby constraining zone boundaries, allowing for continuous updates of the surface model during drilling operations. By avoiding manual operations, the risk of getting a structural model that has diverged from real-time measurements is reduced.

Stochastic facies models based on truncated Gaussian random fields are known for being flexible and well suited to reproduce patterns and features from analogues or conceptual models. In pluri-Gaussian simulation, the number of random fields is theoretically unlimited, which adds flexibility and makes it possible to model a wider range of geological settings. However, the truncation map traditionally used to set up these models quickly becomes unclear when used for higher dimensions. Hence, in practical pluri-Gaussian applications, the number of fields is typically kept as low as two or three. We present a formulation of pluri-Gaussian simulation in which the truncation rule, the function that maps combinations of Gaussian random field values to facies categories, is represented as a particular binary tree. This is used to decouple the fields in the critical Gibbs sampling step of the conditioning process in such a way that we can use multiple lower-dimensional samples instead of a single higher-dimensional sample. The resulting conditioning algorithm scales excellently with the amount of conditioning data and the number of fields. The algorithm accepts a combination of trends and probabilities in the same model setup, which provides additional flexibility in representing varying depositional geometries. We demonstrate the hierarchical pluri-Gaussian simulation with two practical examples. One is based on real data from the Volve oil field in the North Sea. The other combines a large number of synthetic observations with a truncation tree tailored to a more complex geological concept. The choices made when building the truncation tree affect the features of the realizations, especially when it comes to which facies can be in contact and which can overprint each other. This aspect of tree building is discussed in light of the numerical examples given.

We propose a smooth stochastic process for modeling the vertical well path uncertainty. This process describes the accumulation of measurement errors along the well path. We combine the stochastic process with a stochastic model for surfaces into a consistent framework for simultaneous prediction of well paths and surfaces. We show properties of the proposed stochastic process and provide examples of interaction between wells and surfaces.

We demonstrate the use of Ensemble Kalman Inversion (EKI) for building three-dimensional, multi-fault, kinematically restorable structural geologic models, by means of a workflow in which fault geometry, the distribution of slip on a fault, and the geometry of folded horizons are all modeled. The models are constrained by observations of faults and horizons in the present deformed state together with the expectation that horizons should restore flat. Two modeling approaches are tested: restoration from the deformed state, and forward modeling from the restored state. We first test these methods on a synthetic model involving a single fault, and then apply them to a real-field example involving five faults. Models are prone to ensemble collapse, which results in underestimation of uncertainty at small ensemble sizes, but localization and covariance inflation can mitigate this issue. With these methods, EKI can recover the true parameter values in the synthetic case and produce a solution consistent with the data in the real case, as well as quantify uncertainty in both cases. EKI, therefore, shows promise as a tool for building complex, restorable structural geologic models, and it holds the potential for integration of fault kinematics with other ensemble-based subsurface modelling workflows.

Structural restoration using kinematic principles of fault-related folding is a valuable tool in building realistic geological models. Models are, however, typically uncertain and non-unique. While data inversion methods can be employed to find a best-fit model and estimate uncertainty, their use is limited to relatively simple models involving a single fault in two dimensions. In this work, we employ an iterative form of the Ensemble Kalman Filter (EnKF) together with a kinematic model for deformation around normal faults to build and restore three-dimensional structural geologic models. The EnKF is ideally suited to data inversion problems that involve large numbers of model parameters and is frequently used in reservoir simulations, which often do not consider uncertainty in geologic structure. We develop a workflow in which fault geometry, the distribution of slip on a fault, and the geometry of folded horizons are all modelled using the EnKF. The models are constrained by observations of faults and horizons in the present deformed state together with the expectation that horizons should restore flat. We test two modelling approaches: a restoration-based approach in which the model is built in the deformed state and then restored, and a forward modelling-based approach in which the model is built in the restored state and then forward modelled to match present-day data. We test these methods first on a synthetic model involving a single fault and then on a real-world example involving five faults. Both the restoration- and forward modelling-based methods work well for the synthetic model, but forward modelling works best for the more complex real-world case study. The EnKF method provides not only a best-fit model but also an estimate of model uncertainty. The estimation of uncertainty is, however, hindered by the phenomenon of ensemble collapse, which results in underestimation of the uncertainty in model parameters at small ensemble sizes. We employ bootstrap-based localization and covariance inflation to help mitigate this issue and use a dummy parameter to identify whether significant ensemble collapse has occurred. While ensemble collapse remains a challenge in some cases, the EnKF nonetheless shows considerable promise as a tool for building complex many-parameter structural models that are kinematically restorable, and it holds the potential for future integration of structural modelling with other EnKF-based workflows in subsurface modelling.

Truncated Gaussian fields are a common way of modelling facies, where the correlation structure in the Gaussian field defines a spatial correlation structure for the facies. Plurigaussian simulation takes it further by using several underlying Gaussian fields. This allows more flexibility and makes it possible to model a wider range of geological settings, but conditioning can be difficult. We present a fast and accurate implementation of conditional plurigaussian simulation. Our approach has two key elements. The first is to combine complex truncation rules with input facies probabilities. The truncation rule, which is a function from the Gaussian fields to a facies value, can be represented neatly as a binary truncation tree. This allows for a general representation that includes all the traditional 2D truncation masks. We show how to combine the use of such trees with facies probabilities, even in complicated cases with more than two Gaussian fields. The second key element is correct conditioning to all facies observations, not just transitions, by treating them as inequality constraints on the Gaussian fields. We perform inequality Kriging by replacing these facies observations by synthetic observations of the underlying Gaussian fields. To generate synthetic observations that agree with the target posterior distribution, we use a Gibbs sampler. Since this is a quite slow algorithm, we take certain measures to make the calculations faster. Synthetic observations are then used in Kriging, improving the conditioning to facies logs from wells. We demonstrate the method with a synthetic case that combines a large number of observations with the use of a truncation tree tailored from a geological concept.

A COHIBA case study investigating a synthetic model for depth conversion, with focus on how to get the zonation right and the impact of different modelling settings on the estimation of volume distributions.

We have developed a model for the true vertical depth (TVD) uncertainty in wells. The model allows well positions to be predicted given the well uncertainty and surface uncertainties. From this, we can predict the most likely position of the well.

The highest coastal relief on Earth occurs in the Sierra Nevada de Santa Marta in northern Colombia. With an average elevation of ca. 4 km and peaks up to ca. 5.8 km high, this small mountain range lie only 85 km to the south of an abyssal plain ca. 3.5 km deep in the Caribbean Sea. A compilation of sparse bedrock and detrital low‒temperature thermochronometric data, new detrital apatite fission‒track and apatite (U‒Th)/He data from modern river sediment, and stratigraphic patterns of adjacent Miocene ‒ Pliocene basins document an episodic tectonic development of the Sierra Nevada de Santa Marta. Paleocene initial collision of oceanic crust along western Colombia triggered initial exhumation and westward monoclinal tilting of the formerly contiguous Central Cordillera and the Santa Marta Massif. Subsequent late Eocene (ca. 35 Ma) dismembering of both ranges occurred in association with right lateral translation of the Caribbean Plate against the northwestern continental margin of Colombia. This episode marked the onset of contrasting exhumation histories, characterized by low denudation and pediment‒formation in the Central Cordillera, as opposed to rapid, episodic exhumation of the Santa Marta Massif, associated with normal faulting and opening of extensional basins along its southwestern margin. Multiple approaches to extracting exhumation rates from thermochronometry, including 1D and 3D reconstructions, reveal that following rapid late Eocene ‒ early Miocene rock uplift, asymmetric exhumation characterized the Sierra Nevada. On the souhwestern margin, moderate to rapid exhumation favored progradation of alluvial fan deposits on top of underlying shallow marine and fan delta facies. In contrast, diminished exhumation prompted a reciprocal stratigraphy in the northern margin, where facies retrograde, leading to accumulation of shallow marine facies onto fan delta and alluvial fan deposits. Thermochronometric ages of outcropping units, retrieved in modern river sand, imply a very recent (<2 Ma) pulse of exhumation, possibly triggered by removal of lower crust, whose precise magnitudes and time constraints remain unknown.

We applied detrital thermochronometry of modern sediments in a small, high relief mountain range in the Caribbean of northern Colombia, the Santa Marta range (SM), in order to study the patterns of Cenozoic mountain building. New AFT and U-Th/He data from river sand samples of eight catchments draining the eastern flank of the range together with a compilation of published ages and thermokinematic modeling reveal episodic exhumation with decreasing rates to the SE, away from the Caribbean-South American plate boundary. Paleocene-Eocene (60–45 Ma) exhumation is associated with collision of oceanic crust along western Colombia; a late Oligocene-Miocene (30–20 Ma) episode is associated to opening of the Lower Magdalena Valley, and a late pulse at the middle Miocene (16–10 Ma) relates to forward propagation of the deformation toward the Cesar Ranchería basins and the Perijá range, possibly associated to flat subduction. Exhumation rates derived from thermokinematic modeling suggest a post-Miocene acceleration of exhumation.

This user manual describes the COHIBA surface modeling software. It consists of: Part I Introduction: Basic ideas and terminology Part II User manual: Usage, input data and results Part III Tutorials: Special topics such as volumes, simulation and faults Part IV Reference manual: Descriptions of all COHIBA model file elements Part V Theory: Methods used by COHIBA Part VI Appendix: Release notes, known issues, references, list of acronyms, tables and figures, and an index Advanced topics and technicalities are marked by the warning symbol in the right margin. COHIBA model file elements marked by this warning symbol should be used with some care. The latest version of this document is available at: www.nr.no/COHIBA. For COHIBA support contact Pal.Dahle@nr.no or Ariel.Almendral.Vazque@nr.no. The following scientists at Norwegian Computing Center has contributed to the development of COHIBA: Petter Abrahamsen Pål Dahle Frode Georgsen Vera Louise Hauge Gudmund Hermansen Odd Kolbjørnsen Lars Bakke Krogvik Vegard Berg Kvernelv Inge Myrseth Audun Sektnan Arne Skorstad Harald Soleng Ariel Almendral Vazquez Maria Vigsnes Ingrid Aarnes The front page shows two fences along well paths on top of a faulted surface on the Valhall carbonate field in the North Sea. The illustration is made by Ingrid Aarnes. We thank Aker BP for permission to publish the illustration.

Ensemble collapse is one of the main problems encountered when doing history matching using ensemble based methods. In history matching results where ensemble collapse is a problem it is very hard to distinguish updates due to spurious correlation with noise in the data with actual updates attributed to information in the data. Various localization workflows have been proposed for the synthetic case REEK and the public domain dataset from NORNE. We demonstrate moderate improvements of the localized updates for the REEK case. For the NORNE case, issues around the prior distribution were encountered that prevented further investigation of the proposed localization workflow.

Underestimation of posterior parameter uncertainty is one of the main problems encountered when doing history matching using ensemble based methods. In history matching results with the partial or full ensembles collapse, it is very hard to distinguish updates due to spurious correlation with noise in the data from the actual updates attributed to information in the data. History matching of porosity and permeability based on well production data using the ensemble smoother with multiple data assimilation has been performed on a synthetic data set. The presence of ensemble collapse has been evaluated by different means: by looking at the stability of the update based on the starting ensemble, by adding dummy parameters to the update which do not affect the forward model, and by examining how well the data set used to generate the production data matches the posterior distributions of the parameters. Ensemble collapse can be avoided by increasing the number of ensembles. This is however a prohibitively expensive strategy for cases with a large number of history data. Localization methods have been proposed in the literature as a way to increase the ensemble spread and hence avoid collapse, by for example limiting the analysis update to regions of influence of the data, while at the same time keeping the number of ensembles low. A local analysis was performed to reduce the problems related to ensemble collapse. The results from the localized history matching produce a posterior distribution that better matches the original data set. Since our test data set is synthetic, we may perform measures of posterior uncertainty estimation by comparing with the true solution, with and without localization.

Underestimation of posterior parameter uncertainty is one of the main problems encountered when doing history matching using ensemble based methods. In history matching results with the partial or full ensembles collapse, it is very hard to distinguish updates due to spurious correlation with noise in the data from the actual updates attributed to information in the data. History matching of porosity and permeability based on well production data using the ensemble smoother with multiple data assimilation has been performed on a synthetic data set. The presence of ensemble collapse has been evaluated by different means: by looking at the stability of the update based on the starting ensemble, by adding dummy parameters to the update which do not affect the forward model, and by examining how well the data set used to generate the production data matches the posterior distributions of the parameters. Ensemble collapse can be avoided by increasing the number of ensembles. This is however a prohibitively expensive strategy for cases with a large number of history data. Localization methods have been proposed in the literature as a way to increase the ensemble spread and hence avoid collapse, by for example limiting the analysis update to regions of influence of the data, while at the same time keeping the number of ensembles low. A local analysis was performed to reduce the problems related to ensemble collapse. The results from the localized history matching produce a posterior distribution that better matches the original data set. Since our test data set is synthetic, we may perform measures of posterior uncertainty estimation by comparing with the true solution, with and without localization.

We demonstrate accurate prediction of geological surfaces by imposing consistent physical and stochastic relationships between surfaces. The accuracy is improved by using all relevant information collected in wells: well points, zonation in horizontal sections, and gas/fluid content along wells. The conditioned surfaces are used to provide estimates of gross rock volumes of oil and gas reservoirs. In particular, it is shown how knowledge of spill point and zonation along well paths affect trapped volumes. A plain rejection sampling technique is used to deal with the highly non-linear relationships between a surface and its spill point. For well path conditioning, an extension of kriging to treat inequality constraints is proposed. It is based on efficient rejection sampling from a high dimensional truncated multivariate Gaussian distribution. The impact on gross rock volume distributions from different assumptions and data types is demonstrated by examples and the uncertainties in all the involved data types are consistently handled and quantified.

We demonstrate accurate surface predictions by imposing consistent physical and stochastic relationships between surfaces. The accuracy is improved by using all relevant information collected in wells: well markers, zone logs in horizontal sections, and gas/fluid content along wells. The conditioned surfaces are used to provide estimates of gross rock volumes of oil and gas reservoirs. In particular, we show how spill point and zone log information affect trapped volumes. We apply plain rejection sampling techniques to deal with the highly non-linear relationships between a surface and its spill point. For well path conditioning we build upon an extension of kriging to treat inequality constraints, based on an efficient rejection sampling from a high dimensional truncated multivariate Gaussian distribution. A fast approximate approach to simulating surfaces is presented and successfully applied to estimate volumes. The impact on gross rock volume distributions from different assumptions and data types is demonstrated by several examples and the uncertainties in all the involved data types are consistently handled and quantified.